The Uruguayan international then scored deep into injury time to earn Liverpool a 2-2 draw.
"I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea," Suarez told the club's official website.
"I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally.
"I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."
The Football Association has confirmed that it will be reviewing the incident as early as Monday.